Critical Exponent Rigidity for $Θ-$positive Representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911426372698112 |
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| author | Yao, Zhufeng |
| author_facet | Yao, Zhufeng |
| contents | We prove for a $Θ-$positive representation from a discrete subgroup $Γ\subset \mathsf{PSL}(2,\mathbb{R})$, the critical exponent for any $α\in Θ$ is not greater than one. When $Γ$ is geometrically finite, the equality holds if and only if $Γ$ is a lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical Exponent Rigidity for $Θ-$positive Representations Yao, Zhufeng Differential Geometry Dynamical Systems Group Theory 22E40 (Primary) 37AXX (Secondary) We prove for a $Θ-$positive representation from a discrete subgroup $Γ\subset \mathsf{PSL}(2,\mathbb{R})$, the critical exponent for any $α\in Θ$ is not greater than one. When $Γ$ is geometrically finite, the equality holds if and only if $Γ$ is a lattice. |
| title | Critical Exponent Rigidity for $Θ-$positive Representations |
| topic | Differential Geometry Dynamical Systems Group Theory 22E40 (Primary) 37AXX (Secondary) |
| url | https://arxiv.org/abs/2505.17559 |